{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:24:16Z","timestamp":1760145856195,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T00:00:00Z","timestamp":1725667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Found of China","doi-asserted-by":"publisher","award":["61771478"],"award-info":[{"award-number":["61771478"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Digital array radar (DAR) can fully realize digitalization at both the transmitting and receiving ends. However, the development of freedom at the transmitting end is far from mature. So, the new concept of multi-dimensional waveform coding array has appeared, which can optimize the transmitting resources in space\u2013time\/frequency waveform or another dimension. Space\u2013time coding array (STCA) is a typical kind of multi-dimensional waveform coding array, which can make full use of the high degree of freedom at the transmitting end. It realizes emission diversity by introducing a small time delay between different transmission array elements. In this paper, an optimization method for STCA, which combines the array spatial coding at the transmitting end and mismatched filter design at the receiving end, is proposed. This method aims to solve the sidelobe problems of STCA: the inherent resonance phenomenon and the resolution loss problem. The experimental verification and quantitative comparative analysis prove the effectiveness of the proposed method. The resolution is restored to the ideal level under the premise of maintaining the beam-scanning ability and ultra-low sidelobe, and the resonance phenomenon caused by spectrum discontinuity is eliminated simultaneously.<\/jats:p>","DOI":"10.3390\/rs16173322","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T04:15:01Z","timestamp":1725855301000},"page":"3322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Space\u2013Time Coding Array Sidelobe Optimization Method Combining Array Element Spatial Coding and Mismatched Filtering"],"prefix":"10.3390","volume":"16","author":[{"given":"Shenjing","family":"Wang","sequence":"first","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3404-5445","authenticated-orcid":false,"given":"Feng","family":"He","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}]},{"given":"Zhen","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,7]]},"reference":[{"key":"ref_1","unstructured":"Garrod, A. (1995, January 8\u201311). Digital Modules for Phased Array Radar. Proceedings of the IEEE International Radar Conference, Alexandria, VA, USA."},{"key":"ref_2","unstructured":"Cantrell, B., and de Graaf, J. (2001, January 1\u20133). Development of a Digital Array Radar (DAR). Proceedings of the 2001 IEEE Radar Conference, Atlanta, GA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MAES.2013.6575407","article-title":"MIMO SAR imaging: Potential and challenges","volume":"28","author":"Wang","year":"2013","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_4","unstructured":"Younis, M., Krieger, G., and Moreira, A. (2013, January 6\u201311). MIMO SAR techniques and trades. Proceedings of the 2013 European Radar Conference, Nuremberg, Germany."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kim, J., Ossowska, A., and Wiesbeck, W. (2007, January 10\u201312). Investigation of MIMO SAR for interferometry. Proceedings of the European Radar Conference, Munich, Germany.","DOI":"10.1109\/EURAD.2007.4404934"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1109\/TGRS.2013.2263934","article-title":"MIMO-SAR: Opportunities and Pitfalls","volume":"52","author":"Krieger","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2952","DOI":"10.3390\/rs70302952","article-title":"ASTC-MIMO_TOPS mode with Digital Beam-Forming in Elevation for High-Resolution Wide-Swath Imaging","volume":"7","author":"Huang","year":"2015","journal-title":"Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, S., Sun, Y., He, F., Sun, Z., Li, P., and Dong, Z. (2020). DBF Processing in Range-Doppler Domain for MWE SAR Waveform Separation Based on Digital Array-Fed Reflector Antenna. Remote Sens., 12.","DOI":"10.3390\/rs12193161"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/TGRS.2007.905974","article-title":"Multidimensional Waveform Encoding: A New Digital Beamforming Technique for Synthetic Aperture Radar Remote Sensing","volume":"46","author":"Krieger","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1109\/LGRS.2014.2323267","article-title":"Digital Beamforming on Receive in Elevation for Multidimensional Waveform Encoding SAR Sensing","volume":"11","author":"He","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1109\/JSEN.2014.2304720","article-title":"Nonuniform frequency diverse array for range-angle imaging of targets","volume":"14","author":"Wang","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5709","DOI":"10.1109\/JSEN.2016.2573379","article-title":"Transmit beamspace design for multi-carrier frequency diverse array sensor","volume":"16","author":"Gao","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1109\/JSEN.2012.2232909","article-title":"Phased-MIMO radar with frequency Diversity for Range-Dependent Beamforming","volume":"13","author":"Wang","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/TAES.2007.4383581","article-title":"Design principles of MIMO radar detectors","volume":"43","author":"Lops","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5051","DOI":"10.1109\/TSP.2008.928693","article-title":"Diversity-integration trade-offs in MIMO detection","volume":"56","author":"Lops","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6195","DOI":"10.1109\/TSP.2010.2072923","article-title":"Space-Time Coding for MIMO Radar Detection and Ranging","volume":"58","author":"Jajamovich","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/JSEN.2014.2364594","article-title":"Space-time-range adaptive processing for airborne radar systems","volume":"15","author":"Xu","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Babur, G., Aubry, P., and Le Chevalier, F. (2013, January 14\u201316). Space-time codes for active antenna systems: Comparative performance analysis. Proceedings of the IET Radar Conference.","DOI":"10.1049\/cp.2013.0240"},{"key":"ref_19","first-page":"809691","article-title":"Space-time radar waveforms: Circulating codes","volume":"2013","author":"Babur","year":"2013","journal-title":"J. Electr. Comput. Eng."},{"key":"ref_20","unstructured":"Le Chevalier, F., and Savy, L. (2004, January 19\u201321). Colored Transmission for Radar Active Antenna, in Proc. Proceedings of the International Conference on Radar Systems RADAR 2004, Toulouse, France."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zhu, S., He, X., Lan, L., Li, X., and Wang, H. (2023, January 3\u20135). STCA radar multi-dimensional ambiguity function characteristics optimization. Proceedings of the IET International Radar Conference (IRC 2023), Chongqing, China.","DOI":"10.1049\/icp.2024.1313"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102901","DOI":"10.1016\/j.dsp.2020.102901","article-title":"Transmit beampattern synthesis for chirp space-time coding array by time delay design","volume":"110","author":"Wang","year":"2021","journal-title":"Digit. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5994","DOI":"10.1109\/TSP.2021.3114998","article-title":"Space-Time Coding Technique for Coherent Frequency Diverse Array","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1049\/iet-rsn.2015.0311","article-title":"Simple transmit diversity technique for phased array radar","volume":"10","author":"Babur","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1049\/iet-rsn.2016.0595","article-title":"Transmit diversity technique based on joint slow-time coding with circulating code","volume":"11","author":"Li","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lan, L., Liao, G., and Xu, J. (2017, January 8\u201312). Low sidelobes optimization with subarrays for space-time circulating LFMs. Proceedings of the IEEE Radar Conference, Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944174"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Faucon, T., Pinaud, G., and Le Chevalier, F. (2016, January 14\u201316). Mismatched filtering for circulating space-time codes. Proceedings of the IET Radar Conference, Hangzhou, China.","DOI":"10.1049\/cp.2015.1185"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rousse, K., Babur, G., and Le Chevalier, F. (2014, January 19\u201323). Optimization of low sidelobes radar waveforms: Circulating codes. Proceedings of the IEEE Radar Conference, Cincinnati, OH, USA.","DOI":"10.1109\/RADAR.2014.7060290"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"48860","DOI":"10.1109\/ACCESS.2023.3277032","article-title":"Optimization of Mismatched Filters with Asymmetric Side-Lobe Shape for Short-Range MIMO Radars","volume":"11","author":"Karamazov","year":"2023","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1840","DOI":"10.1109\/TAES.2021.3053105","article-title":"Optimization of Diverse PCFM Waveforms and Joint Mismatched Filters","volume":"57","author":"Sun","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1109\/TAES.2018.2871479","article-title":"A Novel Weighted Mismatched Filter for Reducing Range Sidelobes","volume":"55","author":"Sun","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Elhoshy, M., and Youssef, A. (2023, January 18\u201320). Designing High-Performance Mismatched Filters for Radar Applications. Proceedings of the International Telecommunications Conference (ITC-Egypt), Alexandria, Egypt.","DOI":"10.1109\/ITC-Egypt58155.2023.10206161"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/TAES.2007.4383616","article-title":"Pulse Compression sidelobe reduction by minimization of Lp-Norms","volume":"43","author":"Cilliers","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4023","DOI":"10.1109\/TSP.2011.2153199","article-title":"Design of radar receive filters optimized according to Lp-Norms based criteria","volume":"59","author":"Huang","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Rabaste, O., and Savy, L. (2014, January 13\u201317). Mismatched filter optimization via quadratic convex programming for radar applications. Proceedings of the 2014 International Radar Conference, Lille, France.","DOI":"10.1109\/RADAR.2014.7060333"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3107","DOI":"10.1109\/TAES.2015.130769","article-title":"Mismatched Filter Optimization for Radar Applications Using Quadratically Constrained Quadratic Programs","volume":"51","author":"Rabaste","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.sigpro.2011.07.008","article-title":"Minimax robust transmission waveform and receiving filter design for extended target detection with imprecise prior knowledge","volume":"92","author":"Jiu","year":"2012","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1109\/LSP.2020.3021667","article-title":"Joint Design of Transmit Waveform and Mismatch Filter in the Presence of Interrupted Sampling Repeater Jamming","volume":"27","author":"Zhou","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2023.3336053","article-title":"Improved SAR Interrupted-Sampling Repeater Jamming Countermeasure Based on Waveform Agility and Mismatched Filter Design","volume":"61","author":"Zhou","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","first-page":"1","article-title":"Waveform and Filter Joint Design Method for Pulse Compression Sidelobe Reduction","volume":"60","author":"Zhou","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","first-page":"1","article-title":"Low-PSL Mismatched Filter Design for Coherent FDA Radar Using Phase-Coded Waveform","volume":"20","author":"Yu","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1109\/TAES.2016.140556","article-title":"Mismatch filter design via convex optimization","volume":"52","author":"Kajenski","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/17\/3322\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:50:16Z","timestamp":1760111416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/17\/3322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,7]]},"references-count":42,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["rs16173322"],"URL":"https:\/\/doi.org\/10.3390\/rs16173322","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,9,7]]}}}